If in a triangle ABC, the exradii r 1 , r 2 , r 3 are such that r 1 =2r 2 =3r 3 then prove that the triangle is right angled . Also find a:b:c.

Question

SAGAR SINGH - IIT DELHI · Answer

Dear student,
r1=2r2=3r3
Then
r1/6=r2/3=r3/2 =k using ratios
Hence r1=6k,
r2=3k
r3=2k
Hence using the property of solution of trianle the required triangle is equilateral.
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Sagar Singh
B.Tech, IIT Delhi

Nirabhra Agrawal · Answer

Dear Sagar ji,

Will you please solve this question in full as I could not prove the required results with the hints given by you. Few days back I had called and requested you for the same.Thanks.

G P Agrawal

F/o Nirabhra Agrawal

Shashank agrawal · Answer

r1=6r by using a property 1/r1+1/r2+1/r3=1/rAs,r1=stanA/2, r=(s-a)tanA/2 ,So,s/(s-a)=6a=5s/6Similarly,b=2s/3,c=s/2,So,triangle is right angled at A

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If in a triangle ABC, the exradii r 1 , r 2 , r 3 are such that r 1 =2r 2 =3r 3 then prove that the triangle is right angled . Also find a:b:c.

If in a triangle ABC, the exradii r₁, r₂, r₃ are such that r₁=2r₂=3r₃then prove that the triangle is right angled . Also find a:b:c.

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If in a triangle ABC, the exradii r 1 , r 2 , r 3 are such that r 1 =2r 2 =3r 3 then prove that the triangle is right angled . Also find a:b:c.

If in a triangle ABC, the exradii r1, r2, r3 are such that r1=2r2=3r3 then prove that the triangle is right angled . Also find a:b:c.

3 Answers

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If in a triangle ABC, the exradii r₁, r₂, r₃ are such that r₁=2r₂=3r₃then prove that the triangle is right angled . Also find a:b:c.